Electrolyis Concepts deciphered

Happy New year to all IITBandas  . I hope  your Preparation for IIT JEE must be going in full  swing . In this article and in the consecutive article i will try to cover as much concepts as possible which will aid in your Preparation . In this article we will discuss the topic Electrolysis .In the coming articles ,we will also discuss some numerical problems .

In Electrolysis , electrical energy get converted into chemical energy. Here a flow of electricity through a substance may produce a chemical reaction. This process can be shown with the help of following figure. (Here electrolysis of molten NaCl occurs, When Platinum electrodes are dipped into it.)

Here, at anode (+) oxidation occurs, while at cathode (–) reduction occurs.

Faraday’s Laws

The quantitative relationship between the amount of electricity passed through a cell and the amount of substances discharged at the electrodes was systematized by Michael Faraday in the form of the following laws:

First law

The amount of substance discharged at an electrode is proportional to the quantity of electricity passing through the electrolyte.

e.g.

or     … (1)

Z = electrochemical equivalent

It is the number of grams of the substance deposited or dissolved by one coulomb of electricity.

Second Law

When the same quantity of electricity is passed through different solutions, the amounts of different substances deposited or dissolved at the electrodes in different electrolytic cells are proportional to their equivalent weights and in an electrolytic cell, chemically equivalent amount of substances are discharged at both the electrodes.

Charge of 1 mole of electrons = (charge of an electron) × (Avogadro Constant)

= coulombs

= 96500 coulombs

= 26.8 ampere-hour per equivalent

= 1 Faraday

Essential contents of Faraday’s second law is that 1F, which corresponds to 1 mole of electrons, liberates equivalent of matter.

Electrochemical Equivalent and Equivalent weight

The weight in grams of a substance liberated by 1 coulomb of electricity is called electrochemical equivalent (Z)

While the weights in grams liberated by 1F is called gram equivalent weight of the substance.

If and are the equivalent weights of two substances whose electrochemical equivalents are Z₁ and Z₂ respectively, then

… (i)

Now, if the same amount of current is passed for the same interval of time through two different electrolytes then from the first law, i.e.

, we get

Where, and are the weights of the substances deposited from the two electrolytes, the electrochemical equivalents of which are respectively Z₁ and Z₂.

Further

Electrolytic Conductance and Transference

Electrolytic Conductance

As we know that the flow of electricity through solutions of electrolytes is due to the migration of ions when potential difference is applied between two electrodes.

Cations move towards negatively charged electrode , while anions move towards positively charge electrode .

The ease with which electricity flows through a solution is called the conductance (G) of the solution.

Unit Siemen (s) in SI system

Specific Conductance (K)

As we known, Resistance (R) =

Here,

It depends upon the nature of the material

It is the resistance of a specimen 1 cm in length and
1 cm² cross-section.

It is the resistance of 1 cm3 of the material

reciprocal of specific resistance , is called specific conductance (K)

Conductance of 1 cm³ cube of a material

Thus,

unit of

Equivalent conductance ()

Specific conductance, although a suitable property for characterizing metallic conductance, is not so for characterizing electrolytic conductance where the value, amongst other things, depend upon the concentration of the solution of the electrolyte as well

While measuring conductances of electrolytes in solutions, equivalent conductance, is frequently used.

Equivalent conductance is the conducting power of all the ions produced by 1 gm–equivalent of an electrolyte in a given solution.

Relation between Specific Conductance and Equivalent conductance

Suppose we take 1 c.c of solution of an electrolyte placed between two large electrodes 1 cm apart. The cross sectional area of the solution will be 1 cm². The conductance of the solution will evidently be its specific conductance because we are having one cubic centimeter of the solution.

Further, suppose that 1 c.c. of solution contains 1 gm equivalent of the electrolyte dissolve in it

Then, according to the definition given above, the conductance of the solution will be equal to the equivalent conductance.

Hence, conductance = specific conductance (K)

= Equivalent conductance

Suppose the solution is now diluted to 1000 c.c. we will be having now 1000 c.c. of the solution. The conductance of the resulting solution, therefore will be 1000 times its specific conductance. But even now as the solution contains only 1 gm-equivalent of the electrolyte between the electrodes, the conductance measured will be equivalent conductance. Thus

If the solution is further diluted to say, 5000 C.C. there will be 5000 c.c. of the solution and hence,

In general,

Here, is the volume of the solution in cm³ containing 1 gm-equiv. of the electrolyte.

Unit of :

Molar Conductance : 

It is the conducting power of all the ions produced by one mole of the electrolyte in a given solution.

Unit

Cell constant (K_cell)

Unit (m^–1)

Variation of molar conductance
with dilution

Molar conductance of an electrolyte increases with increase in dilution due to increase in degree of dissociation of electrolyte.

Increase in the number of ions on dilution is much lesser than increase in the volume of the solution. Hence no of ions per unit volume actually decreases. Hence, specific conductance decreases, although molar conductance increases on progressive dilution

• The variation of molar conductance with dilution in some common electrolytes is shown below in fig. As can be seen, in strong electrolytes there is a tendency for molar conductance to approach a certain limiting value when the concentration approaches zero.
  

The molar conductance at this point is known as molar conductance at zero concentration or at infite dilution. It is denoted by

Infinite dilution is meant a solution so dilute that it has maximum or limiting molar conductance which does not increase on further dilution.

This value, in the case of strong electrolytes, is obtained by extrapolating the molar conductance graph to zero concentration.

In the case of weak electrolytes, however, there is no indication that a limiting value can be attained even when the concentration approaches zero. Hence, it is not useful to obtain the limiting value by extrapolating in the case of weak electrolytes.

There is an indirect method for obtaining molar conductance at infinite dilution for weak electrolytes which is based on Kohlrausch’s law.

Assuming that increase in molar conductance on dilution is due only to increase in the degree of dissociation of the electrolyte, which is evident when limiting value of molar conductance is approach the dgree of dissociation is unity. Hence at any other concentration, when the molar conductance is say, ^_m, the degree of dissociation will be given by

Ionic Mobility

We have seen that, at infinite dilution, all electrolytes are completely dissociated, their molar conductances differ vastly from one another.

This is due to differences in speeds of ions e.g. the molar conductance at infinite dilution of HCl acid is more than three times as high as that of NaCl. Since, ion is common, it follows that the speed of ion is more than three time the speed of ion.

• Since, the speed of an ion varies with the potential applied, so we use the term ionic mobility.
  

  
  

  It is the distance travelled by an ion per second under a potential gradient of 1 volt/meter.
  

  Transport Number
  

  Experimentally it has been seen that, the number of ions discharged at each electrode depends upon the sum of the speed or mobilities of two ions.
  

  
  

  Since according to Faraday’s first law of electrolysis, the number of ions discharged at an electrode is proportional to the total quantity of electricity passed through the solution. Hence.
  

  
  

  
  

  • The fraction of the total current carried by each ion is called its transport number. Thus, if u₊ is the mobility of cation and u_– that of anion, then
    

  
  

  Transport number of cation (t₊) =
  

  Similarly,
  

  Again.